1st order The ODE

Is there any tutorial to solve 1st order ode using rung kutta 4th order method without using ode45

Answer 1

[Jan]

Of course. Either use one of the other integrators, e.g. ode15s. Although it is designed for stiff ODEs, you can process nin-stoff ODEs also. You find a lot of other integrators in the net also, e.g. in the FileExchange. Matlab offers a bunch of integrators with fixed step sizes also: https://www.mathworks.com/matlabcentral/answers/98293-is-there-a-fixed-step-ordinary-differential-equation-ode-solver-in-matlab-8-0-r2012b

You can use a cheap Euler method only: Determine the current slope by evaluating the ODE, then compute: x(i+1) = x(i) + df * h.

For my lessons of numerical maths it was a homework to write out own Runge Kutta solver. This takes less than an hour.

[Mohammad Adeeb]

What i mean is without using any built in function with mat lab , i have to use a function tha i have to define

[Jan]

Without using built-in functions you cannot do anything useful in Matlab. I assume only the integrator is meant.

Of course you can write your own Runge Kutta integrator. You do not need a tutorial to do this, but just some basic experiences in Matlab and the definition of the algorithm. You find tutorials for learning Matlab in the net, search e.g. for "Matlab onramp". Examples for integrators can be found also, because this is a standard homework for beginners in numerical maths.